Puffy things are swollen or soft, like a big, puffy hairdo or your favorite puffy winter coat that's stuffed full of feathers.
Your eyes might be puffy after a really sad movie, and your cat may look puffy when she's hissing at the dog. Big, round clouds are puffy, and so are the white seed heads of dandelions — the puffy balls you can blow on and make a wish. Wind is puffy too, when it blows in little gusts. This is the earliest meaning of puffy, from puff and its Old English root pyffan, "to blow with the mouth."